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Results tagged with elliptic-pde
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user 161514
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
3
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0
answers
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References on smoothness of minimal surfaces in Riemannian manifolds
It's well known that $C^1$ minimal surfaces (surfaces that are locally area minimzing) in $\mathbb{R}^n$ are automatically smooth, and one can prove this result by solving the Dirichlet problem of the …
- 438
3
votes
1
answer
269
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Does the strong maximum principle for minimal surfaces hold in Riemannian manifolds?
In Euclidean spaces, the following maximum principle for minimal surfaces are well known.
Theorem: If $\Sigma_1$, $\Sigma_2 \subset \mathbb{R}^n$ are complete connected minimal hypersurfaces, $\Sigma_ …
- 438
2
votes
0
answers
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A question on the maximum principle of second order elliptic equations
Let $Lu=a^{ij}u_{ij} + b^i u_i$ be an elliptic operator of second order in a bounded domain $\Omega$. Assume that $a^{ij}$ is uniformly elliptic. Then it's well known that the following maximum princi …
- 438